I'm native to DFW area and attended UT Austin. Here are my thoughts. Full disclosure: I'm a road biker and I HATE hill climbing.
Austin: Sure, a great mecca for off-the-wall bike shops, but the heavy HEAVY traffic congestion, hills and summer heat? Pass. I've done the much-lauded river/lake trails and found them unimpressive and, in many places, unpaved. Real estate pricing is also quite insane.
Lubbock: Charming little college town but the roads are in terrible shape! You'd need a full-suspension mountain bike here! Ditto on other small towns ... see more details below.
Dallas: The bike culture is growing. I can ... and have ... biked from the north Plano area, all the way down to its infamous White Rock Lake trail, through downtown Dallas and down south into Oak Cliff (which is turning into Portland) ... about 40 miles ... using safe paved bike paths and some residential streets.
Personally, what I find pleasant for cycling is not the heart of a major metropolitan city and its social-engineered bike paths and lanes, but the outskirts of them: expansive suburbs with smooth, paved, low-density streets around them. Currently I live in the McKinney/Allen area north of DFW and do rides from my doorstep.
The problem with smaller towns away from major cities is, though charming, there is a very limited amount of suburban streets, and often in awful condition, and you have to risk riding on the narrow farm-to-market roads with 70 to 90 mph traffic buzzing around you.
Be curious to hear other's opinions on other cities ... always looking to throw the bike in the trunk and head off for some different scenery nearby.